Linear extensions, projections, and split faces

Abstract

The main result is essentially: Let F be a closed split face of a compact convex set K such that A( F) is separable and has the (positive) metric approximation property. Then there is a (positive) linear extension operator from A( F) into A( K) of norm one. This is applied to C ∗-algebras thus giving sufficient conditions for the existence of right inverses to surjective ∗-homomorphisms.